We present a greedy version of an existing metaheuristic al-gorithm for a special version of the Cutting Stock Problem(CSP). For this version, it is only possible to have indirectcontrol over the patterns via a vector of continuous valueswhich we refer to as a weights vector. Our algorithm itera-tively generates new weights vectors by making local changesover the best weights vector computed so far. This allows usto achieve better solutions much faster than is possible withthe original metaheuristic.